The distance between pair of parallel lines represented by $$ x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0 $$ is. units
The distance between pair of parallel lines represented by
$$
x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0
$$
is. units
$5 \sqrt{2}$
$5 \sqrt{2} a$
$2 \sqrt{5} a$
$a$
Solution
Given, $\because x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0$ represents a pair of parallel lines.
Compare with standard form
$
\begin{aligned}
& a x^2+b y^2+2 h x y+2 g x+2 f y+c=0 \\
& a=1, b=1, h=1, g=-4 a, f=-4 a, c=-9 a^2
\end{aligned}
$
$\because$ We know that distance between the parallel lines.
$
\begin{aligned}
D & =2 \sqrt{\frac{g^2-a c}{a(a+b)}} \\
& =2 \sqrt{\frac{(-4 a)^2-(1)\left(-9 a^2\right)}{1(1+1)}} \\
& =2 \sqrt{\frac{16 a^2+9 a^2}{2}}=2 \sqrt{\frac{25 a^2}{2}}=2 \times \frac{5 a}{\sqrt{2}}=5 \sqrt{2} a
\end{aligned}
$